STAT 1043 Homework 1

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New Brunswick Community College, Fredericton *

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1043

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Statistics

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Feb 20, 2024

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STAT 1043 Managerial Statistics II Homework 1 – Pieces of the Puzzle Please submit through Dropbox by 5:30 pm on Thursday, January 18, 2024 Goal: Shake off some dust on things that might have happened in STAT 1 Directions: Please label your solutions properly and write as clearly as you can. Please ensure that the solutions are written in order. Collaboration in solving problems on the assignments are acceptable; however, copying assignments is inappropriate and will be considered academic misconduct. For the calculation questions, it’s fine to use Excel or other software, but please take a picture/screenshot of your setup with the final answer or explain what you did on the software in writing to get your result. Activity: (The part to hand in for marks) 1. (2 marks) The accounting department at a mail-order company counted the following number of incoming calls per day to the company’s toll-free number during the first seven days in January: 14, 24, 17, 31, 36, 26, 17 COMPUTATION: Sample mean = Sum of all the values in the sample Number of values in the sample SAMPLE MEAN x = Σx N [3–2] x is the sample mean. It is read “x bar.” n is the number in the sample. x represents any particular value. Ʃ is the Greek capital letter “sigma” and indicates the operation of adding. Ʃx is the sum of the x values in the sample. Calculate the mean number of incoming calls over this period. [Text ref: 3.3 sample mean] 2. (2 marks) The following number of bags of cookies were eaten by Cookie Monster last week:

13, 5, 10, 6, 8 Find the standard deviation of the sample. [Text ref: 3.11 sample variance and sample standard deviation] 3. (4 marks) Let z be the standard normal random variable. Use Table B.1 or Excel to find the probabilities below: a. Find the area under the curve to the right of the z value z = 0 b. Find the area under the curve to the right of the z value z = 1.96 c. Find the area under the curve to the left of the z value z = -1.65 [Text ref: 6.4 The standard normal probability distribution] 4. (6 marks) The average time it takes to walk to McAllister Mall from my house is Normally distributed with a mean of 12.2 minutes and a standard deviation of 2.5 minutes. a. What is the z-value associated with 14.3 minutes? b. What is the probability that it takes between 12.2 and 14.3 minutes for me to walk to the mall? c. What is the probability that it takes me less than 10 minutes to walk to the mall? [Text ref: 6.4 Finding areas under the normal curve] Additional Practice Problems (these do not need to be handed in, and are optional/not for marks) 1. The blood groups of 238 people are distributed as follows: 66 have type A blood, 79 have B blood type, 74 have O blood type, and 19 have type AB blood. a. If a person from this group is selected at random, what is the probability that this person has an O blood type? b. If a person from this group is selected at random, what is the probability that this person has an AB blood type? c. Would you consider either of these outcomes (being of a specific blood group) to represent a “rare event”? Explain using your answers from (a) and (b). 2. Review the simulation for the sampling distribution of the sample means ( https://onlinestatbook.com/stat_sim/sampling_dist/ ) Describe what you see under the following scenarios: a. Parent Population: Normal, 10,000 samples, Mean N=10 b. Parent Population: skewed, 10,000 samples, Mean N= 25 c. Parent Population: Custom (make your own, describe the shape after you make it), 10,000 samples, Mean N= 20

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